1. Trigonometry for Angle
Geometry Right Triangles Lesson 5

2. Trigonometry For Angles - Notes
Sine
Cosine
Tangent
inverse
angle

3. Trigonometry for Angles - Notes
Sin
Sin-1
Cos
Cos-1
Tan
Tan-1
degree

4. Class Example 1 S 𝑶 𝑯 C 𝑨 𝑯 T 𝑶 𝑨 𝐬𝐢𝐧 𝒙= 𝟏𝟓 𝟐𝟒 𝐬𝐢𝐧 −𝟏 𝒙 𝐜𝐨𝐬 −𝟏 𝒙
I have… two sides.
I need… an angle.
Class Example 1 H A
Set up the proper inverse trig ratio. O
𝐬𝐢𝐧 𝒙= 𝟏𝟓 𝟐𝟒
S 𝑶 𝑯
C 𝑨 𝑯
T 𝑶 𝑨
𝐬𝐢𝐧 −𝟏 𝒙
𝐜𝐨𝐬 −𝟏 𝒙
𝐭𝐚𝐧 −𝟏 𝒙

5. Class Example 2 S 𝑶 𝑯 C 𝑨 𝑯 T 𝑶 𝑨 𝐜𝐨𝐬 𝒙= 𝟖 𝟏𝟏 𝐬𝐢𝐧 −𝟏 𝒙 𝐜𝐨𝐬 −𝟏 𝒙
I have… two sides.
I need… an angle.
Class Example 2 A O
Set up the proper inverse trig ratio. H
𝐜𝐨𝐬 𝒙= 𝟖 𝟏𝟏
S 𝑶 𝑯
C 𝑨 𝑯
T 𝑶 𝑨
𝐬𝐢𝐧 −𝟏 𝒙
𝐜𝐨𝐬 −𝟏 𝒙
𝐭𝐚𝐧 −𝟏 𝒙

6. Class Example 3 S 𝑶 𝑯 C 𝑨 𝑯 T 𝑶 𝑨 𝐭𝐚𝐧 𝒙= 𝟐𝟎 𝟑𝟕 𝐬𝐢𝐧 −𝟏 𝒙 𝐜𝐨𝐬 −𝟏 𝒙
I have… two sides.
I need… an angle.
Class Example 3 O A
Set up the proper inverse trig ratio. H
𝐭𝐚𝐧 𝒙= 𝟐𝟎 𝟑𝟕
S 𝑶 𝑯
C 𝑨 𝑯
T 𝑶 𝑨
𝐬𝐢𝐧 −𝟏 𝒙
𝐜𝐨𝐬 −𝟏 𝒙
𝐭𝐚𝐧 −𝟏 𝒙

7. Student Example 1 S 𝑶 𝑯 C 𝑨 𝑯 T 𝑶 𝑨 𝐬𝐢𝐧 −𝟏 𝒙 𝐜𝐨𝐬 −𝟏 𝒙 𝐭𝐚𝐧 −𝟏 𝒙
Set up the proper inverse trig ratio.
S 𝑶 𝑯
C 𝑨 𝑯
T 𝑶 𝑨
𝐬𝐢𝐧 −𝟏 𝒙
𝐜𝐨𝐬 −𝟏 𝒙
𝐭𝐚𝐧 −𝟏 𝒙

8. Student Example 2 S 𝑶 𝑯 C 𝑨 𝑯 T 𝑶 𝑨 𝐬𝐢𝐧 −𝟏 𝒙 𝐜𝐨𝐬 −𝟏 𝒙 𝐭𝐚𝐧 −𝟏 𝒙
Set up the proper inverse trig ratio.
S 𝑶 𝑯
C 𝑨 𝑯
T 𝑶 𝑨
𝐬𝐢𝐧 −𝟏 𝒙
𝐜𝐨𝐬 −𝟏 𝒙
𝐭𝐚𝐧 −𝟏 𝒙

9. Student Example 3 S 𝑶 𝑯 C 𝑨 𝑯 T 𝑶 𝑨 𝐬𝐢𝐧 −𝟏 𝒙 𝐜𝐨𝐬 −𝟏 𝒙 𝐭𝐚𝐧 −𝟏 𝒙
Set up the proper inverse trig ratio.
S 𝑶 𝑯
C 𝑨 𝑯
T 𝑶 𝑨
𝐬𝐢𝐧 −𝟏 𝒙
𝐜𝐨𝐬 −𝟏 𝒙
𝐭𝐚𝐧 −𝟏 𝒙